Combine the strawberries and sugar in a small bowl and let sit for about 20 minutes, until the mixture is very wet.
Combine the mixture with the pineapple juice in a blender or food processor and purée.
Set a strainer over a small bowl and scrape the purée into the strainer, so that the liquid drains into the bowl below. Stir the purée gently as it strains to get as much liquid as possible without forcing any solids into the strained liquid. Discard the solids, reserving the liquid. You should have about 2 cups.
The purée can be stored in the refrigerator for up to 1 day, but is best if used immediately.
Mix with Seltzer:2/3 cup strawberry pineapple purée2/3 cup seltzer1 serving
Spoon the purée into a tall glass.
Add the seltzer and stir just until blended.
Add ice and serve.To Carbonate with a Siphon:2 cups water1 batch strawberry pineapple purée 3 servings
Combine the water and purée in a 1-quart soda siphon. Charge with CO2 according to the manufacturer's directions. Siphon-charged sodas can be stored in the siphon in a refrigerator for up to 5 days. Disperse as desired into tall glasses filled with ice, and serve.